CN107872256A - Blind Detecting and modulation constellation optimization method, storage medium in wireless light communication - Google Patents
Blind Detecting and modulation constellation optimization method, storage medium in wireless light communication Download PDFInfo
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Abstract
The invention discloses the extensive MIMO in communication technical field（Multiple‑Input Multiple‑Output）In outdoor radio optical communication system, maximum likelihood blind checking method and transmitting modulation constellation Optimization Design based on channel statistical information.In the case of dual-mode antenna number is extensive, receiving end signal approximation Gaussian distributed is determined according to central-limit theorem and law of great number first, and then the principal component of the asymptotically optimal decision threshold of reception signal for obtaining any order of modulation, the then average error sign ratio of foundation system：Exponential damping item, using the criterion of minimum each several part exponential damping coefficient is maximized to modulating Constellation Design, system is set to be averaged error sign ratio minimum, the method finally solved using iterative numerical, the modulation constellation optimized, hence it is evident that improve systematic function.The present invention carries out optimum detection and modulation constellation optimization design merely with the statistical information of channel to receiving and transmitting signal, compared to conventional method, systematic function can be significantly improved, and approach the systematic function of known channel information, there is relatively low overhead simultaneously, so as to improve the feasibility of the method in actual applications.
Description
Technical Field
The invention relates to a blind detection design method and an emission modulation constellation optimization design method in the technical field of Communication, in particular to a method for optimally detecting a transmitting and receiving signal and optimally designing a modulation constellation by utilizing statistical information of a channel in a large-scale MIMO Outdoor Wireless Communication (OWC) Communication system.
Background
With the rapid development of wireless communication technology, the wireless optical communication technology effectively alleviates the problem of shortage of wireless spectrum resources. Meanwhile, the wireless optical communication technology has the advantages of safety, greenness, simple equipment and the like, has been widely paid attention and researched in recent years, and will become an important part in the future wireless communication technology. The massive MIMO technology has been adopted by the 5 th generation mobile communication as one of the key core technologies, which can greatly reduce power and improve system performance and coverage. In a wireless optical communication system, an LED (Light-Emitting Diode) array is adopted at a transmitting end, and a PD (Photo-Diode) array is adopted at a receiving end, so that a convenient condition is provided for the introduction of a large-scale MIMO (multiple input multiple output) technology, the communication efficiency of the system is effectively improved, the system is simple to realize, and the large-scale MIMO technology becomes an excellent choice of the wireless optical communication system.
The channel in the indoor OWC system is generally slowly changed, while the channel in the outdoor OWC system is mainly influenced by atmospheric turbulence and atmospheric attenuation, and under the condition of weak turbulence, the channel model is usually lognormal distribution; in case of strong turbulence, the channel model is often a dual gamma distribution. The environment of an outdoor channel is complex and changeable, random attenuation is caused to optical signals, and the transmission performance of the optical signals is seriously influenced. Meanwhile, in a large-scale MIMO outdoor wireless optical communication system, estimating channel information by using pilot frequency brings about a great system overhead, and reduces system transmission efficiency. The blind detection method based on the channel statistical information and the optimal design method of the emission modulation constellation are researched, the system overhead can be greatly reduced, the system performance can be kept, and the method has important theoretical significance and practical value.
Disclosure of Invention
Problems to be solved
The technical problem to be solved by the present invention is to provide a blind detection method based on channel statistics information and an optimal design method of a transmit modulation constellation in a large-scale MIMO outdoor wireless optical communication system, which are used for blind detection of a received signal to solve the problems in the prior art.
(II) technical method
In order to solve the technical problem, the invention adopts the following technical method:
the blind detection and modulation constellation optimization method in the wireless optical communication comprises the following steps:
s1: in the large-scale MIMO outdoor wireless optical communication system, each sub-channel is independently and identically distributed, the first-order statistical information and the second-order statistical information of known channels at the transmitting end and the receiving end are used for transmitting power modulation signals, and the receiving end carries out blind detection on the received signals by using a maximum likelihood criterion according to the statistical information; the statistical information comprises a mean and a variance;
s2: based on the maximum likelihood criterion, obtaining the asymptotic optimal decision threshold of the received signal with any modulation order under the condition of large antenna number of a transmitting end and large antenna number of a receiving end respectively;
s3: according to the asymptotic optimal decision threshold, under the condition of optical signal non-negative constraint and average optical power constraint, the average symbol error rate is minimizedThe main components of (A): and the exponential attenuation item is used for carrying out optimization design on the modulation constellation by using an optimization criterion of maximizing the exponential attenuation coefficient of each part, and finally, a numerical iteration solving method is used for obtaining the optimized modulation constellation.
Further, in the S1:
the model of the large-scale MIMO outdoor wireless optical communication system with the number of transmitting end antennas being M and the number of receiving end antennas being N is as follows: y = Hs + n;
wherein
y is a received signal matrix of dimension N × 1;
h is a channel matrix of dimension N multiplied by M, each sub-channel of the channel matrix is independently and identically distributed, and the first-order and second-order statistical information of known channels at two ends including mean value mu is transmitted and received according to other distributions such as lognormal distribution or Rayleigh distribution h Sum varianceh is a channel mark and indicates that the mean value and the variance are the mean value and the variance of the channel;
n is a noise matrix of Nx 1 dimension, each element in the noise matrix is independently and identically distributed, the obedient mean value is 0, and the variance is(ii) a gaussian distribution of; n is a noise marker indicating a variance ofIs the variance of noise
s is a signal matrix of M multiplied by 1 dimension of the transmitting terminal;
the transmitting end sends an L-order power modulation signal, wherein a modulation constellation set [ s ] 1 ,s 2 ,…,s L ]The elements in the modulation constellation are not negative and are arranged in the order from small to large, the transmission probability of each element in the modulation constellation is the same, and the constraint of average optical power is satisfied:P T represents the average transmitted optical power, s k ∈[s 1 ,s 2 ,…,s L ]K =1,2, \ 8230;, L; blind detection of the received signal is performed using a maximum likelihood criterion.
Further, in S2, under the condition that the number of the transmitting and receiving antennas is large, the maximum likelihood is performed on the mean value of the received signals according to the central limit theorem and the large theoremDetection of mean value of received signalCan be expressed as
Wherein
Equivalent channelApproximately obey a Gaussian distribution with i =1,2, \8230;, N, j =1,2, \8230;, M, the mean and variance of which are respectively μ h ，
Equivalent noiseObeying a gaussian distribution, with a mean and variance of 0 respectively,
mean value of received signalObeying a Gaussian distribution with mean and variance of μ h s k ，Wherein
Deciding a signal based on a maximum likelihood detection criterionExpressed as:
wherein, the first and the second end of the pipe are connected with each other,representing the received signal as s with respect to the transmitted signal k Conditional probability density function of time, i.e.
Asymptotic optimum decision threshold th of received signal k The expression of (a) is:
(1) When the number of antennas at the receiving end is large,
whereink =1,2, \ 8230;, L; from s k+1 >s k Andtherefore, it is not only easy to useIs equivalent toThe optimal decision threshold is in the non-equal interval characteristic and is obtained at the same timeThe relationship of (1);
(2) When the number of antennas at the transmitting end is large,
the optimal decision threshold is characterized by equal intervals.
Further, in S3, based on the maximum likelihood blind detection criterion, the average symbol error rate of the systemExpressed as:
p ek expressing the symbol error rate of the received signal corresponding to the kth constellation point detected in the L-order power modulation, and averaging the symbol error rate through algebraic transformation according to the characteristics of a progressive optimal decision threshold and a Gaussian probability density functionIs further expressed as:
wherein, the first and the second end of the pipe are connected with each other,as an error function, in case of a large scale of the receiving-end antenna,is an exponential decay coefficient; in the case of a large scale of the transmitting-end antenna,
further, in S3, the specific step of obtaining the optimized modulation constellation includes:
step (1): assigning an initialization step value to the exponential decay term coefficient d, and making the lowest level of the transmitting signal s for optimizing the transmitting power 1 ＝0；
Step (2): when k =1, the coefficient is exponentially attenuatedFind a th 1 Is then calculated byFinding an s 2 A value of (d); the equation is satisfied for all constellation points and detection thresholds:
from this analogy to find s 3 ，s 4 ，…，s L All the L constellation points and L-1 detection threshold values;
and (3): calculating the average optical power of the emission constellation obtained in the step (2)If it is less than the average optical power constraint P T Increasing d by a step value and repeating the step (2);
and (4): repeating steps (2) and (3) until the average optical power of the resulting emission constellation is close to or equal to the average optical power constraint P T (ii) a At this time, the obtained constellation points and the detection threshold are numerical approximate solutions of the optimization problem.
A storage medium having stored thereon computer instructions adapted to be executed by a processor, the computer instructions, when executed by the processor, performing a method.
(III) advantageous effects
Aiming at a large-scale MIMO outdoor wireless optical communication system, the blind detection method carries out modulation constellation optimization design on the average symbol error rate of the system by using the criterion of maximizing the minimum exponential attenuation coefficient of each part, and obtains an optimized modulation constellation by using a numerical iteration solution method. The invention does not need instantaneous channel information at the transmitting and receiving ends, utilizes the statistical information of the channel to carry out optimal detection and modulation constellation optimization design on the transmitting and receiving signals, and obviously improves the system performance with lower system overhead under the condition of unchanged transmitting total power, thereby improving the feasibility of the method in practical application.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a transmission diagram of a massive MIMO outdoor wireless optical communication system according to the present invention.
Fig. 3 is a comparison graph of the average symbol error rate performance of the system when the blind detection method and the conventional mean detection method of the present invention vary with the number of receiving antennas under different snr conditions.
Fig. 4 is a comparison graph of the average symbol error rate performance of the system when the blind detection method and the known channel information detection method of the present invention vary with the number of receiving antennas under different snr conditions.
Fig. 5 is a comparison graph of the average symbol error rate performance of the system when the blind detection method, the conventional mean detection method and the known channel information detection method of the present invention vary with the number of receiving antennas under poor channel conditions under different snr conditions.
Fig. 6 is a comparison chart of the average symbol error rate performance of the system when the improved average value detection method and the conventional average value detection method of the present invention vary with the number of transmitting antennas under different snr conditions.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
In a large-scale MIMO outdoor wireless optical communication environment, each sub-channel experiences a complex and variable channel environment, which causes random attenuation to optical signals, and at this time, estimating the channel by using a pilot signal may cause a large system overhead. Under the condition of large-scale number of receiving and transmitting antennas, optimal detection and modulation constellation optimization design are carried out on the receiving and transmitting signals only by utilizing the statistical information of the channels so as to optimize the average symbol error rate of the system, but the performance of the system is limited by the number of transmitting end antennas and the number of receiving end antennas, wherein the number of the receiving end antennas is a main influence factor. Under the condition that the total transmission power is not changed, the system performance is obviously improved by using lower system overhead, so that the feasibility of the method in practical application is improved.
Based on the above reasons, in order to achieve the purpose of obviously improving the system performance with lower system overhead, the invention provides a blind detection method based on channel statistical information and an optimal design method of a transmitting modulation constellation.
Referring to fig. 1, the method comprises the following steps:
s1: in the large-scale MIMO outdoor wireless optical communication system, each sub-channel is independently and identically distributed, obeys other distributions such as lognormal distribution or Rayleigh distribution and the like, and receives and transmits first-order and second-order statistical information of known channels at two ends, wherein the statistical information comprises a mean value and a variance. The transmitting end transmits power modulation signals, and the receiving end does not need instantaneous channel information and only uses the maximum likelihood criterion to carry out blind detection on the received signals.
S2: under the condition that the number of the receiving and transmitting antennas is large, according to the existing central limit theorem and the existing large number theorem, the received signals approximately obey Gaussian distribution, and on the basis of the maximum likelihood detection criterion, under the condition that the number of the transmitting end antennas and the number of the receiving end antennas are large, asymptotic optimal judgment thresholds of the received signals with any modulation order are obtained respectively; under the condition that the number of the receiving end antennas is large, the optimal judgment threshold is in a non-equal interval characteristic; and under the condition that the number of the antennas at the transmitting end is large, the optimal judgment threshold is equally spaced.
S3: according to the asymptotic optimal decision threshold, under the conditions of non-negative constraint of optical signals and average optical power constraint, optimally designing a modulation constellation to minimize the average symbol error rate of the system, wherein the specific implementation method is thatMinimizing average symbol error rateThe main components of (A): performing exponential decay items, performing optimal design on the modulation constellation by using an optimization criterion of maximizing the exponential decay coefficient of each part at the minimum, and finally obtaining an optimized modulation constellation by using a numerical iteration solution method; when the number of the antennas at the receiving end is large, the optimal modulation constellation is in a non-equal interval characteristic, and when the number of the antennas at the transmitting end is large, the optimal modulation constellation is in an equal interval characteristic.
The following is a detailed description of the implementation of the above-described method of the present invention.
In the large-scale MIMO outdoor wireless optical communication system, the number of transmitting end antennas is M, the number of receiving end antennas is N, and the system model can be expressed as:
y＝Hs+n
wherein y is a received signal matrix of dimension N × 1; h is a channel matrix with dimension of N multiplied by M, each sub-channel in the channel matrix is independently and identically distributed and follows other distributions such as lognormal distribution or Rayleigh distribution, the first-order and second-order statistical information of the known channels of the receiving end and the transmitting end comprise mean value mu h Sum varianceh is the channel label, indicating the mean value μ h Sum varianceMean and variance of the channel; n is a noise matrix of Nx 1 dimension, each element in the noise matrix is independently and identically distributed, the obedient mean value is 0, and the variance isA gaussian distribution of (d); n is a noise mark indicating a variance ofIs the variance of the noise; s is a signal matrix of M × 1 dimension at the transmitting end.
LaunchingThe end sends L-order power modulation signal, modulation constellation set [ s ] 1 ,s 2 ,…,s L ]The elements in the modulation constellation are not negative and are arranged in the order from small to large, the transmission probability of each element in the modulation constellation is the same, and the constraint of average optical power is satisfied:P T represents the average transmitted optical power, where s k ∈[s 1 ,s 2 ,…,s L ]K =1,2, \ 8230;, L. The receiving end does not need instantaneous channel information and only uses the maximum likelihood criterion to carry out blind detection on the received signal.
Under the condition of large number of receiving and transmitting antennas, the maximum likelihood detection is carried out on the arithmetic mean value of the received signals according to the central limit theorem and the majority theorem, and the mean value of the received signals isCan be expressed as:
wherein the equivalent channelApproximately follows a Gaussian distribution with mean and variance of μ h ，Equivalent noiseObeying a gaussian distribution, with a mean and variance of 0 respectively,thus the mean value of the received signalApproximately obey a Gaussian distribution, each of whichThe value and variance are respectively mu h s k ，Wherein
Deciding a signal based on a maximum likelihood detection criterionCan be expressed as:
wherein the content of the first and second substances,representing the received signal as s with respect to the transmitted signal k Conditional probability density function of time, i.e.Respectively obtaining the asymptotic optimal decision threshold th of the received signal with any modulation order under the condition of large-scale number of antennas at the transmitting end and the receiving end k Expression (c):
(1) When the number of antennas at the receiving end is large,
whereink =1,2, \8230;, L. From s k+1 >s k Andtherefore, it is not only easy to useIs equivalent toTherefore, the optimal decision threshold presents the non-equal interval characteristic and can be obtained at the same timeThe relationship (2) of (c).
(2) When the number of antennas at the transmitting end is large,
the optimal decision threshold is characterized by equal intervals.
Average symbol error rate of system based on maximum likelihood blind detection criterionCan be expressed as:
p ek and the symbol error rate of the received signal corresponding to the detection kth constellation point in the L-order power modulation is represented. According to the characteristics of the progressive optimal decision threshold and Gaussian probability density function, the average symbol error rate is obtained through algebraic transformationMay be further expressed as:
wherein the content of the first and second substances,for the error function, in case of a large number of antennas at the receiving end,is an exponential decay factor, and in the case of a large number of transmit antennas,
in the above S3, for the case of large number of antennas at the receiving end, under the conditions of non-negative optical signal constraint and average optical power constraint, the specific implementation method for optimally designing the modulation constellation to minimize the average symbol error rate of the system is to minimize the average symbol error rateThe main components of (A): and the exponential attenuation item is used for carrying out optimization design on the modulation constellation by using an optimization criterion of maximizing the exponential attenuation coefficient of each part, and finally, a numerical iteration solving method is used for obtaining the optimized modulation constellation.
The method comprises the following specific steps:
step (1): assigning a very small initialization step value to the exponential decay term coefficient d, e.g. 1 x 10 -2 Or 1X 10 -3 . For optimizing the transmission power, the lowest level of the transmitted signal s is set 1 ＝0。
Step (2): when k =1, the coefficient is exponentially attenuatedFind a th 1 Is then calculated byFinding an s 2 The value of (c). The equation is satisfied for all constellation points and detection thresholds:
from this analogy to find s 3 ，s 4 ，…，s L All L constellation points and L-1 detection threshold values.
And (3): calculating the average optical power of the emission constellation obtained in the step (2)If it is less than the average optical power constraint P T Then d is increased by one step value and step (2) is repeated.
And (4): repeating steps (2) and (3) until the average optical power of the resulting emission constellation is close to or equal to the average optical power constraint P T (ii) a At this time, the obtained constellation points and the detection threshold are numerical approximate solutions of the optimization problem. The average optical power of the emission constellation is close to or equal to the average optical power constraint P T The explanation is as follows: mean optical power and mean optical power constraint P in the transmit constellation T When the constellation points and the detection threshold are equal, the obtained constellation points and the detection threshold are approximate solutions of optimal numerical values of the optimization problem; while the average optical power in the transmit constellation approaches the average optical power constraint P infinitely T In the process of (3), the smaller the difference between the two is, the better the numerical approximation solution is; on-average optical power and average optical power constraint P of emission constellation T When the difference value is larger, the approximate solution of the constellation point and the detection threshold value can still be obtained, but the average symbol error rate performance of the system is poorer; the degree of proximity, i.e., the difference, between them is flexibly set according to the specific situation when calculating.
When the number of the antennas at the receiving end is large, s is easily obtained according to the relation between the constellation point and the optimal judgment threshold k+2 -th k+1 >th k -s k To convert the inequality into s k+2 -s k+1 -th k+1 >th k -s k -s k+1 Because of th k +th k+1 ＝2s k+1 Carry-in inequality as k+2 -s k+1 >s k+1 -s k Therefore, the optimal modulation constellation is characterized by non-equal intervals.
For the case when the number of transmit side antennas is large,k =1,2, \ 8230;, L, the optimal modulation constellation is equally spaced.
In the traditional mean value detection, the decision threshold is characterized by equal intervals, namelyThe average symbol error rate of the system is:the invention is based on the maximum likelihood blind detection of the channel statistical information, the optimal decision threshold presents the non-equal interval characteristic, namelyThe average symbol error rate of the system is:and non-equal interval modulation constellations are obtained through optimization, and the average symbol error rate performance of the system is improved to the maximum extent.
Referring to the comparison diagram of the average symbol error rate performance of the system shown in fig. 3, in a large-scale MIMO outdoor wireless optical communication system, the number of antennas at the transmitting end is configured to be 2, a channel model satisfies a lognormal distribution with a parameter σ of 0.3, 8-order unequal-interval power modulation signals are transmitted, a receiving end performs performance comparison by using a blind detection method based on channel statistical information and a conventional mean detection method, as is apparent from fig. 3, under the condition that SNR is 0db,5db and 10db respectively, the average symbol error rate performance of both systems is improved along with the increase of the number of receiving antennas, but the blind detection method based on the channel statistical information is obviously superior to the conventional mean detection method.
Referring to the comparison diagram of the average symbol error rate performance of the system shown in fig. 4, in a large-scale MIMO outdoor wireless optical communication system, the number of antennas at the transmitting end is configured to be 2, a channel model satisfies a lognormal distribution with a parameter σ of 0.3, 8-order unequal interval power modulation signals are transmitted, a receiving end performs performance comparison by using a blind detection method based on channel statistical information and a detection method of known channel information, and it is obvious from fig. 4 that the average symbol error rate performance of the system by using the blind detection method based on the channel information and the detection method of the known channel information is close to each other under the condition that the SNR is 0db,3db and 6db respectively.
Referring to the comparison diagram of the average symbol error rate performance of the system shown in fig. 5, in a large-scale MIMO outdoor wireless optical communication system, the number of antennas at the transmitting end is 128, a channel model satisfies a lognormal distribution with a parameter σ of 1, and 8-order unequal-interval power modulation signals are transmitted, and the receiving end performs performance comparison by using a blind detection method based on channel statistical information, a detection method of known channel information and a conventional mean detection method, as is apparent from fig. 5, under the conditions that the SNR of signal-to-noise ratios is 0db,3db,6db and channel conditions are poor, the average symbol error rate performance of the system by using the blind detection method based on channel information and the detection method of known channel information is very close, and the performance of the system by using the conventional mean detection method is much smaller than that of the former two.
Referring to the comparison diagram of the average symbol error rate performance of the system shown in fig. 6, in a large-scale MIMO outdoor wireless optical communication system, the number of antennas at a receiving end is configured to be 2, a channel model satisfies a lognormal distribution with a parameter σ of 0.3, a 2-order unequal interval power modulation signal is sent, the receiving end compares the performance of the receiving end by using an improved mean detection method and a conventional mean detection method, and it is obvious from fig. 6 that, under the condition that the SNR of the signal-to-noise ratio is 0db,3db and 6db, the average symbol error rate performance of the system by using the improved mean detection method and the conventional mean detection method approaches, but both the average symbol error rate of the system tends to the lower limit of the performance along with the increase of the number of transmitting antennas.
The present invention also provides a storage medium having stored thereon computer instructions adapted to be executed by a processor, the computer instructions, when executed by the processor, performing the above-described method of the present invention.
The storage media may include various forms of computer-readable media such as volatile memory, semiconductor memory, magnetic media memory, and so forth.
One or more computer program instructions are stored on a storage medium and executable by a processor to perform at least one of the methods disclosed herein for blind detection and constellation optimization. Various data can be stored in the storage medium and used for a processor to directly call the method for implementing the invention.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the overall concept of the present invention, and these should also be considered as the protection scope of the present invention.
Claims (6)
1. The blind detection and modulation constellation optimization method in wireless optical communication is characterized by comprising the following steps:
s1: in the large-scale MIMO outdoor wireless optical communication system, each sub-channel is independently and identically distributed, the first-order statistical information and the second-order statistical information of known channels at the transmitting end and the receiving end are used for transmitting power modulation signals, and the receiving end carries out blind detection on the received signals by using a maximum likelihood criterion according to the statistical information; the statistical information comprises a mean and a variance;
s2: based on the maximum likelihood criterion, obtaining the asymptotic optimal decision threshold of the received signal with any modulation order under the condition of large antenna number of a transmitting end and large antenna number of a receiving end respectively;
s3: according to the asymptotic optimal decision threshold, under the condition of optical signal non-negative constraint and average optical power constraint, the average symbol error rate is minimizedThe main components of (A): and the exponential attenuation item is used for carrying out optimization design on the modulation constellation by using an optimization criterion of maximizing the exponential attenuation coefficient of each part, and finally, a numerical iteration solving method is used for obtaining the optimized modulation constellation.
2. The method according to claim 1, wherein the method for blind detection and modulation constellation optimization in wireless optical communication comprises:
in the S1:
the model of the large-scale MIMO outdoor wireless optical communication system with the number of transmitting end antennas being M and the number of receiving end antennas being N is as follows: y = Hs + n;
wherein
y is a received signal matrix of dimension N × 1;
h is a channel matrix of NxM dimension, each sub-channel of the channel matrix is independently and identically distributed, follows other distributions such as lognormal distribution or Rayleigh distribution and the like, and receives and transmits first-order and second-order statistical information of known channels at two ends, including mean value mu h Sum varianceh is a channel mark and indicates that the mean value and the variance are the mean value and the variance of the channel;
n is a N multiplied by 1 dimensional noise matrix, and each element in the noise matrix is independently and identically distributed, subject to a mean value of 0 and a variance of(ii) a gaussian distribution of; n is a noise mark indicating a variance ofIs the variance of noise
s is a signal matrix of M multiplied by 1 dimension of the transmitting terminal;
the transmitting end sends an L-order power modulation signal, wherein a modulation constellation set [ s ] 1 ,s 2 ,…,s L ]The elements in the modulation constellation are not negative and are arranged in the order from small to large, the transmission probability of each element in the modulation constellation is the same, and the constraint of average optical power is satisfied:P T represents the average transmitted optical power, s k ∈[s 1 ,s 2 ,…,s L ]K =1,2, \ 8230;, L; using maximum likelihood criterionBlind detection is performed on the received signal.
3. The method according to claim 2, wherein the method for blind detection and modulation constellation optimization in wireless optical communication comprises:
in S2, under the condition of large number of the receiving and transmitting antennas, the maximum likelihood detection is carried out on the mean value of the received signals according to the central limit theorem and the numerator theorem, and the mean value of the received signals isCan be expressed as
Wherein
Equivalent channelApproximately obey a Gaussian distribution with i =1,2, \8230;, N, j =1,2, \8230;, M, the mean and variance of which are respectively μ h ，
Equivalent noiseObeying a gaussian distribution, with a mean and variance of 0 respectively,
mean value of received signalObeying a Gaussian distribution with mean and variance of μ h s k ，Wherein
Deciding signals based on maximum likelihood detection criteriaExpressed as:
wherein the content of the first and second substances,representing the received signal as s with respect to the transmitted signal k Conditional probability density function of time, i.e.
Asymptotically optimum decision threshold th of received signal k The expression of (a) is:
(1) When the number of antennas at the receiving end is large,
whereinFrom s k+1 >s k Andtherefore, it is possible toIs equivalent toThe optimal decision threshold is in the non-equal interval characteristic and is obtained at the same timeThe relationship of (1);
(2) When the number of antennas at the transmitting end is large,
the optimal decision threshold is characterized by equal intervals.
4. The method according to claim 3, wherein the method for blind detection and modulation constellation optimization in wireless optical communication comprises:
in S3, based on the maximum likelihood blind detection criterion, the average symbol error rate of the systemExpressed as:
p ek representing the symbol error rate of the received signal corresponding to the detection k constellation point in the L-order power modulation, and averaging the symbol error rate through algebraic transformation according to the characteristics of the gradual optimal decision threshold and the Gaussian probability density functionIs further expressed as:
wherein the content of the first and second substances,as an error function, in case of a large scale of the receiving-end antenna,is an exponential decay coefficient; in the case of a large scale of the transmitting-end antenna,
5. the method according to claim 4, wherein the method comprises:
in S3, the specific step of obtaining the optimized modulation constellation is:
step (1): assigning an initialization step value to the exponential decay term coefficient d, and making the transmitting signal s with the lowest level for optimizing the transmitting power 1 ＝0；
Step (2): when k =1, the coefficient is decayed exponentiallyFind a th 1 Is then calculated byFinding an s 2 A value of (d); the equation is satisfied for all constellation points and detection thresholds:
from this analogy to find s 3 ，s 4 ，…，s L All the L constellation points and L-1 detection threshold values;
and (3): calculating the emission obtained in step (2)Average optical power of constellationIf it is less than the average optical power constraint P T Increasing d by a step value and repeating the step (2);
and (4): repeating steps (2) and (3) until the average optical power of the resulting emission constellation is close to or equal to the average optical power constraint P T (ii) a At this time, the obtained constellation points and the detection threshold are numerical approximate solutions of the optimization problem.
6. A storage medium having stored thereon computer instructions adapted to be executed by a processor, the computer instructions, when executed by the processor, performing the method of any one of claims 1 to 5.
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